Nilpotent orbits and Whittaker functions for derived functor modules of Sp(2, ℝ)

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Abstract

We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp (2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in g* and the asymptotic support of the cohomological representation.

Original languageEnglish
Pages (from-to)769-794
Number of pages26
JournalCanadian Journal of Mathematics
Volume54
Issue number4
Publication statusPublished - 2002 Aug

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Whittaker Function
Nilpotent Orbits
Generalized Functions
Functor
Orbit
Subgroup
Module
Character

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nilpotent orbits and Whittaker functions for derived functor modules of Sp(2, ℝ). / Miyazaki, Takuya.

In: Canadian Journal of Mathematics, Vol. 54, No. 4, 08.2002, p. 769-794.

Research output: Contribution to journalArticle

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